An efficient hybrid method for modeling lipid membranes with - - PowerPoint PPT Presentation
An efficient hybrid method for modeling lipid membranes with molecular resolution G.J.A. (Agur) Sevink, M. Charlaganov & J.G.E.M Fraaije Japan, 2010 Soft Matter Chemistry Group, Leiden University, The Netherlands Thanks to : C.D. Chau, A.V.
Japan, 2010
G.J.A. (Agur) Sevink, M. Charlaganov & J.G.E.M Fraaije Soft Matter Chemistry Group, Leiden University, The Netherlands Thanks to: C.D. Chau, A.V. Zvelindovsky, organizers!
Japan, 2010
Japan, 2010
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“Cell membrane dynamics essentially lipidic” (100+ simulation papers)
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Vesicle fusion induced by coiled-coil motif (short peptide fragments)
Hana Robson Marsden et al, A reduced SNARE model for membrane fusion,
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slow collapse growth (coalescence) micellar growth fast fast Ostwald ripening & vesicle fusion and fission closure extremely slow fast
(2002) Europhys. Lett.
Nm and mm: model for complete vesicle and/or vesicle fusion requires considerable coarse graining Efficient, realistic, dynamic
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10-15 10-12 10-9 10-6 10-3 100 10-10 10-9 10-8 10-7 10-6 10-5 10-4
(fs) (ps) (ns) (µs) (ms)
Mesoscale methods Atomistic Simulation Methods Semi-empirical methods Ab initio methods
Monte Carlo molecular dynamics tight-binding MNDO, INDO/S
Methods
Based on SDSC Blue Horizon (SP3) 512-1024 processors 1.728 Tflops peak performance CPU time = 1 week / processor
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20% A2B2 in a selective bad solvent METHOD: DDFT= mean-field SCFT+diffusion
AS., Zvelindovsky A.V. Macromolecules 38 7502-7513 (2005).
Movie 200 nm 100 nm
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Beyond block copolymers: How to realistically represent lipids? Increasing complexity? ‘Floppy’ Gaussian chains: onion vesicles Mean-field: concentrated systems
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DDFT: pattern formation dynamics in concentrated BCP (quasi)equilibrium behavior, AB, ABC, branced Phase transition under external fields (confinement, shear, E, etc)
I
V
2 Entropic: Gaussian chains in self- consistent field U Enthalpic: mean-field interactions (FH) Pressure term, incompressible
local kinetic model processing conditions noise
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Experiment Calculation
nucleation annihilation splitting
High-speed SFM measurements of membrane dynamics: ~ sec ptf
Structural transition due to thickness reduction : top view
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chemical fragment spring solvent
Variable composition DDFT: Underlying harmonic spring, calculations and interactions field-based Particles (DPD): Harmonic spring, angle and torsion potentials, soft core repulsive pair potentials
distance
c
0 + Δaij
liquid incompressibility
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cIk
I,k
K( r − rk)ρI ( r )
V
d r
k] = F DDFT[ρI ]+ U particles[
k]+ F coupling[ρI,
k]
Diffusion, timescales are more or less comparative (coupled update)
k = Dk[ fk conserv −
I
V
k random(t)
k
particles fields
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r ρΙ(r) Positive c
Coupling force: away from high density field values Coupling chemical potential: field diffuses away from regions with many particles
Advantage is possibility to mix different representations on CG level for same or different constituents: sparse (particles) + abundant (field) Mapping: besides FH parameter (χ)/interaction strengths (a) we need compressibility ( ) and coupling ( ).
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Determine ‘free’ parameters by requiring thermodynamic consistency for single bead solvent in both representations.
: match either pressure or excess chemical potential
determine FH χ and Groot & Warren to convert to soft-core potential strength Note: both particles and fields adapt dynamically
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Use these values and realistic DPD lipid parameters
DPD, Shillcock and Lipowky 2002 (realistic) Hybrid calculation where the solvent is replaced by a field, with the same S&L parameters for the lipid
(163)
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Averaging over many initial condition and time frames
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Preliminary: analytical equilibrium solution for solvent (field) can be converted into an additional potential in particle description
I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E, 011506 (2005).
k sol,
k lipid ) mapping
k lipid ) analytic
k lipid
CGMD, implicit solvent
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Diffusion is patient (DPD – O(20000)) Experiments: slow process!
323
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Steepest descent Newton method Quasi-Newton method
Fluctuation-dissipation
Curvature-dependent mobility
Optimization in numerical mathemetics (objective function) Diffusion in statistical mechanics (potential function)
+ spurious drift
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Φ(x) ~ k 2 x 2
M = k−1 = (∇2Φ)−1
drift term noise term ~ k-1
Stability analysis: independent of k
Sparse sampling Dense sampling
dx = −kxdt + 2kBTdW (t) dx = −xdt + 2 kBT k dW (t)
M =1
for for
slow modes fast modes
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T
Rouse chain
Additional costs per timestep but
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Analysis for quadratic potential (Rouse chain): all modes evolve equally fast (real-space Fourier acceleration)
Φ = 1 2 Φbond + 1 2 Φbending + Φdihedral + ΦLJ
Bead=amino acid (either neutral, hydrophobic or hydrophilic) Minimal model of a protein Conclusions (S-QN): Enhanced sampling of energy landscape (many inherent states) Hierarchical optimization (bond length, angles, torsions, non bonded) Generic S-QN method: accelerated but no ’realistic’ dynamics
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Conclusions: New hybrid model for particle/field mixtures Reuse DPD parameters for CG lipids Possibility of implicit solvent (analytic) Additional sparse constituents can be added as CG particle chains New S-QN method to speed up formation kinetics To do: Validate membrane material parameters in hybrid model Concise derivation of implicit solvent Implementation and parameterization of SNARE-like CG proteins Outlook: Large scale simulations Vesicle fusion …
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(a.sevink@chem.leidenuniv.nl)
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Principles of SQN 29
29 Principles of SQN
‘native state’
One basin Several basins
Principles of SQN 30
30 Principles of SQN
Native state: left, turn and right sub-domains native
Equilibration order: bonds, angles, torsions, LJ (even for reduced spring constants)